Title: Order-Preserving Braids

Abstract: Consider your favorite torsion-free group. Then, try to order the elements of the group in a way that isn’t changed by the group operation. A group that can be ordered this way is called bi-orderable. Now, consider an automorphism of your group. If that automorphism leaves a bi-ordering of the group unchanged, the automorphism is called order-preserving. An interesting topological situation where order-preservingness problems arise is when a braid acts on the fundamental group of a punctured disk. We will discuss how eigenvalues can be used to answer questions about order-preserving braids. This project is joint work with Khanh Le. This project was partially supported by the NSF grant DMS-2213213.

https://www.shsu.edu/directory/employee-profiles/johnson-jonathan-jcj055